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Differential Geometry of Manifolds

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Matsievsky S.V.

A geometric model of linear fractional transformations

DOI
10.5922/0321-4796-2022-53-8
Pages
84-93
linear fractional transformation complex plane three-di­men­sional projective space forbidden quadric parabolic cone funda­men­tal group

Abstract

A model of linear fractional transformations of the complex plane in the form of points of the complex three-dimensional projective space without a linear “forbidden” quadric is presented. A model of real linear fractional transformations of the complex plane in the form of points of the real three-di­mensional projective space without a linear “forbidden” quadric is presented. A geometric separation of points corresponding to parabolic, hyperbolic and elliptic real linear fractional transformations by a “parabolic” cone touching the forbidden quadric is found. Some pro­per­ties of model points corresponding to real linear fractional transfor­ma­tions are found. Some properties of model points corresponding to fun­da­men­tal groups transformations of biconnected domains of the complex pla­ne are found.

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